4D nanoimaging of early age cement hydration

Despite a century of research, our understanding of cement dissolution and precipitation processes at early ages is very limited. This is due to the lack of methods that can image these processes with enough spatial resolution, contrast and field of view. Here, we adapt near-field ptychographic nanotomography to in situ visualise the hydration of commercial Portland cement in a record-thick capillary. At 19 h, porous C-S-H gel shell, thickness of 500 nm, covers every alite grain enclosing a water gap. The spatial dissolution rate of small alite grains in the acceleration period, ∼100 nm/h, is approximately four times faster than that of large alite grains in the deceleration stage, ∼25 nm/h. Etch-pit development has also been mapped out. This work is complemented by laboratory and synchrotron microtomographies, allowing to measure the particle size distributions with time. 4D nanoimaging will allow mechanistically study dissolution-precipitation processes including the roles of accelerators and superplasticizers.


All Data Open access data
Tomography and laboratory raw data 7

Table S1
Chemical analysis by X-ray fluorescence 8 Table S2 Rietveld quantitative phase analysis of the Portland cements 8 Table S3 Textural details for the two cements 8 Supplementary  Table S4 Selected cumulative heat release data from isothermal calorimetry 8 Tables  Table S5 Rietveld quantitative phase analysis for the hydrating paste 9 Table S6 Mean β values converted to µ, and the resulting w/c ratios 9 Table S7 Mass and electron densities values for selected components 10 Table S8 Component segmentation and average electron densities from PXCT 11 Table S9 Volume percentages for the hydrating pastes by the used techniques 12

Figure S1
Laboratory Rietveld plots for the anhydrous cements 13 Figure S2 Lab-µCT selected orthoslice and grey-value profile 14 Figure S3 Syn-µCT selected orthoslice and grey-value profile 14 Figure S4 PXCT selected orthoslice and grey-value profile 15 Figure S5 Lab-µCT Fourier Shell Correlation plots 16 Figure S6 Syn-µCT Fourier Shell Correlation plots 17 Figure S7 PXCT Fourier Shell Correlation plots 18 Figure S8 PXCT electron density and absorption orthoslices 19 Figure S9 Bivariate histograms of electron densities and absorption indexes 20 Figure S10 VOI histogram of the electron densities for PXCT 20 Figure S11 Second etch-pit evolution picture 21 Figure S12 PXCT vertical views showing the paste evolution 22 Figure S13 Etch-pit growth rates variability 23 Supplementary Figure S14 2D view of PXCT and electron density profile, first example 24 Figures Figure S15 Alite dissolution and C-S-H gel densification for the first example 24 Figure S16 2D view of PXCT and electron density profile, second example 25 Figure S17 Alite dissolution and C-S-H gel densification for the second example 25 Figure S18 2D view of PXCT and electron density profile, third example 26 Figure S19 2D view of PXCT and electron density profile, fourth example 26 Figure S20 PXCT vertical views showing the water/air porosity evolution 27 Figure S21 Machine Learning training flow chart 28 Figure S22 C-S-H shell segmentation flow chart 29 Figure S23 Comparison of the C-S-H shell raw data and segmentation output 29 Figure S24 PXCT orthoslices showing water/air porosity evolution, second example 30 Figure S25 PXCT orthoslices showing water/air porosity evolution, third example 30 Figure S26 PXCT orthoslices showing selected features of the paste evolution 31 Figure S27 PXCT vertical views for a fast dissolving particle 31 Figure S28 Capillary water porosity evolution 32

Synchrotron X-ray computed microtomography experiment (Syn-µCT).
Microtomographic scans were acquired at the 150 m-long beamline ID19 of the European Synchrotron (ESRF) in Grenoble, France. A so-called single-harmonic undulator (type: u17.6, gap 16.5 mm) was chosen as a source due to its excellent photon flux density at a narrow bandwidth around approximately 19 keV photon energy. The u17.6 allows beamline ID19 to be operated only with the two mandatory windows (0.8 mm diamond in the front-end and 0.5 mm Beryllium in the experimental hutch) and an 0.7 mm-thick Aluminium attenuator and hence, guaranties a homogeneous wave front: which is suited for high-sensitivity measurements by means of inline propagation-based phase contrast. The propagation distance between sample and detector was set to 15 mm. The indirect high-resolution detector consisted of a so-called revolver-microscope by the French company OptiquePeter (Lentilly, France) 1 , the system lens-couples an 8.7 µm-thin LSO:Tb (Tb-doped Lu2SiO5) single-crystal scintillator with a 10× Olympus microscope (0.3NA) to a sCMOS-based camera (type: pco.edge, PCO AG, Germany) 2 . The effective pixel size of the detector assembly is approximately 0.6 µm. 6000 projection angles were acquired over a 360 degree tomographic scan with an exposure time of 0.05 s, i.e. 5 minutes scan, at ~21.5 °C. During this experiment, the ESRF operated in so-called 4bunch timing mode with a reduced ring current of maximum 20 mA. The estimated flux density at the sample position was 4.2×10 11 photons . s -1. mm -2 . Phase retrieval of the projections was performed using the Paganin algorithm 3 , considering the ratio of the refractive and absorption index / equal to 70. In order to retrieve the microstructural content introduced by the inherent smoothing characteristics of the phase retrieval method, a Gaussian unsharp mask was applied. The voxel size with the employed configuration, to fully image a capillary of 0.7 mm of diameter, was 0.65 µm.
The tomographic reconstructions were performed using the open-source tomography software available at the ESRF, relying on the sub-packages NXtomoMill and NABU 4 . Given its straightforward Graphics Processing Unit (GPU)-based implementation, the full volume reconstructions were performed on the Power9 cluster using the gold-standard filtered back projection (FBP) algorithm. The projections are first corrected for beam profile illumination (flat field), dark current noise of the detector (dark field) and filtered for any potential pixel outliers arising from stray photons. The reconstructed volume, consisting of 2490×2490×1950 pixels, is cast to 16 bit format considering the 10-90% of the volume histogram and cropped to the region of interest. In the case of the reconstructions used for the Fourier Shell Correlation (FSC) analysis, 5 the original reconstruction is split into two sub-sampled reconstructions considering the number of the reconstructed either even or odd projections.

Near-field ptychographic X-ray computed tomography (PXCT).
The measurements were carried out with a high-stability instrument designed for high-resolution PXCT working in air and at room temperature 6,7 , using a photon energy of 8.93 keV. The coherent illumination was defined with a Fresnel zone plate (FZP) of 120 µm diameter and 60 nm outer-most-zone width, which at this energy had a focal distance of 51.9 mm. The FZP had locally displaced zones, specifically designed to produce an optimal illumination for ptychograph 8 . The flux of the X-ray beam was 1.7×10 8 photons . s -1 at the sample position. The sample was placed at 13 mm downstream the focus, where the illumination had a size of about 30 µm. Ptychographic scans were recorded following the positions of a Fermat spiral 9 with an average step size of 6 or 7 µm and a field of view of 186 µm × 30 µm (horizontal × vertical). The field of view must be larger than the size of the capillary to include an air region at both sides of the sample, which is needed for successful tomographic reconstructions and for quantitative contrast. At each scanning position, magnified images of the sample were recorded with an in-vacuum Eiger 1.5M detector 10 with a pixel size of 75 µm placed at 5.237 m downstream the sample, with an acquisition time of 0.1 s. A scan speed of ∼5 Hz was achieved thanks to a combined motion of the FZP and the sample, while achieving an effective static illumination on the sample during acquisition 11 . Near-field ptychographic scans were repeated at 420 rotation angles of the sample in equal intervals from 0 to 180 deg. We recorded a total of 3 tomograms at different times from the start of the cement hydration at ∼25 °C, the temperature of the experimental hutch. The first tomogram was recorded with an average scanning step size of 6 µm, it started at 17 h and finished at 20h and 55 minutes, after water mixing, i.e. 3h 55 min of total acquisition time. This scan is hereafter labelled 19 h dataset. The other two tomograms were recorded with a step size of 7 µm lasting 3h 6 min. The scans labelled 47 and 93 h started at 46 and 92 h (after water mixing), respectively. The scan times include the dead time during motion of stages in between acquisitions. The dose absorbed by the specimen during data acquisition was estimated to be 0.7 and 0.5 MGy for the tomograms with 6 and 7 µm of step size, respectively.
Near-field ptychographic reconstructions were performed for each projection using the Ptycho Shelves package 12 developed by the Coherent X-ray Scattering group at PSI, using 5000 iterations of a difference map algorithm 13 adapted for near-field geometry. The pixel size of the images, determined by geometric magnification, is 186.64 nm and we estimate by Fourier ring correlation 5 that the 2D resolution of each reconstructed image is about 200 nm. For each tomographic dataset, projections were aligned with subpixel accuracy and processed for phase tomographic reconstruction from phase projections as previously reported 14,15 . The 3D spatial resolution was estimated by FSC 5 . The resolution obtained, see subsection dedicated to the spatial resolution, was limited by the number of projections, which was chosen to have reasonable scan times.
PXCT provides 3D maps of the electron density of the specimen with quantitative contrast, the sensitivity being about 0.02 e -Å -3 . 16 For attaining quantitative electron densities, the entire specimen must be included in the field of view, containing some empty space around it, which was the case in our measurements. Therefore, it is possible to easily distinguish air and water regions in the specimen, which have electron densities of 0.00 and 0.33 e -Å -3 , respectively. Obviously, neutron imaging is the standard technique to disentangle water from air porosities. 17 A key advantage of neutron imaging is its ability to can scan large volumes. However, it must also be noted that at inferior spatial resolution compared to PXCT.

Tomographic data analysis.
Initially, the re-alignment of the data, when needed must be detailed.
For the PXCT, the capillary position was very accurate, as the capillary/holder system was mounted from the tray storage to the sample stage by the flOMNY gripper (robot). Hence, the angular orientation of the sample was maintained. The field of view of the sample was aligned carefully based on features visible in the 2D projections. The scanned regions with time were consistent within a few voxels and therefore no alignment between different acquisitions was required.
For the Syn-µCT, a mark was drawn on the sample holder and sample stage for the incident beam to minimise the initial incidence angular position variability. Before each scan, a projection was acquired as a reference for the next one in order to scan the same region. A minor manual registration was required, mostly rotations around x-and y-axes.
For the Lab-µCT, manual registration was required to align the different acquisitions. The process is described next. The capillary was considered as a cylinder and we manually made the cylinders vertical and centred in the reconstructed volume. The remaining rotation around the z-axis was visually done by superimposing distinguishable landmarks in the corresponding images.
The segmentation was done on a Volume of Interest (VOI) corresponding to the inner part of the capillaries for each imaged sample. The total volume of these VOIs varies depending on the sample sizes, amounting to ∼1×10 5 μm 3 for each PXCT dataset and ∼1×10 8 μm 3 for Syn-µCT and Lab-µCT samples. A supervised Machine-Learning (ML) image analysis approach was used to segment the different components of the scanned samples, using the IPSDK Explorer software (version 3.2.0.0 for Windows™, Reactiv'IP, Grenoble, France). This software allows us to manually label voxels on a selected training dataset (approximately 31 voxels for each component on average for PXCT, 20 voxels on average for Syn-µCT and Lab-µCT) and to rapidly obtain test results to determine if the labelling is sufficient or if it requires more information/retraining. The initial classification was based on the electron densities with a variation of ∼5% of the measured values, from selected volumes, which are given in Table S7. These test results are obtained after a first learning step using a random forest method. It is also possible for the user to keep or remove features used in the random forest decision trees based on their relevance. This method permitted to segment the components with comparable grey values and/or electron densities, overlaid ML models on raw datasets are shown in Fig. 7.
On the one hand, the good contrast and the high spatial resolution in PXCT allowed to classify the components into seven categories. They are given next from higher to lower electron densities: i) C4AF (yellow) with highest values; ii) C3S/C2S/C3A (dark brown) which are the clinker particles; iii) calcite (pink); iv) portlandite (green); v) the rest of the hydrated phases with lower electron densities were labelled as 'Low-Density Hydrates' (light brown), i.e. C-S-H gel, iron-silicon-hydrogarnet, hemicarbonate and ettringite; vi) water porosity (blue); and vii) air porosity (black). On the other hand, due to the contrast and spatial resolution limitations in the two other modalities, Syn-µCT and Lab-µCT, the components were classified into four categories. The classification from higher to lower grey-values was: i) clinker particles (dark brown), i.e. C4AF/C3S/C2S/C3A; ii) a component labelled 'High-Density Hydrates' (green), being mainly portlandite and calcite; iii) another component labelled 'Low-Density Hydrates' (light brown), being mainly C-S-H gel, iron-silicon-hydrogarnet, hemicarbonate and ettringite; and iv) porosity (black) which contain both water and air. It is noted that Syn-µCT and Lab-µCT microtomographies do not allow to distinguish water from air porosities due to the similarities in their X-ray attenuation values.
This ML approach also permits to mitigate the influence of partial volume effects in-between labelled components for accurate quantitative analysis of PXCT, i.e. mean electron density. Selected results after the PXCT segmentation procedure are summarised SI. Movie 1. In addition, after grains were segmented using the ML approach described above, the C-S-H gel shell thickness was computed on PXCT imaged sample at 19 h, see Fig. 6 and SI. Movie 2. The wall thickness script computes the object thickness. For a given pixel, the thickness is the radius of the largest circle centred on this pixel entirely included in the object. The steps of the data analysis process are shown in flowcharts, see Fig. S20 and S21. A further postsegmentation data analysis calculation was carried out in order to show the particle size distribution evolution with hydration time. The anhydrous cement particles, at the three hydration times, were classified by computing their mean Feret diameters. Fig. 8b displays the volume percentage of the segmented grains (and their cumulative volumes) as function of the particle sizes that can be compared with the initial characterization by laser diffraction, see

Spatial resolution analysis.
The spatial resolution was characterised by two approaches as recently reported 18 . On the one hand, it can be determined from the grey-value changes in line profiles through the edge sharpness of the interfaces. A point spread function (PSF) used to determine the spatial resolution of the images as ISO/TS 24597 defines the Gaussian radius of the PSF as the resolution, which equals to a change between 25 %-75 % grey value along the studied interfaces. 19 Here, a common interface present in the three imaging modalities has been selected for the line profiles: the glass capillary wall -air (i.e. exterior of the capillaries). We have measured 25 interfaces in every tomogram, which allowed us to determine the average spatial resolution and its associated standard deviation. On the other hand, FSC plots 5 have been also computed. The traces are displayed in Figures S5-S7 giving spatial resolution values of 430 nm, 470 nm, 500 nm, 650 nm and 1.9 µm, for PXCT-19h, PXCT-47h, PXCT-93h, Syn-µCT and Lab-µCT datasets, respectively. Moreover, the FSC trace for PXCT-19h shows a smooth decrease in the 0.0-0.2 spatial frequency range, which is likely due to the hydration of cement during the 4-hour measurement. As expected, this behaviour is not shown at later ages.
It should be noted that the agreement between the spatial resolution results between the edge sharpness approach and FSC method is satisfactory for Syn-µCT (750 vs. 650 nm) and Lab-µCT (2.2 vs.1.9 µm) datasets.
However, the agreement between these two approaches is not good for PXCT (for instance, 250 vs 430 nm at 19 h). The poorer resolution estimated by FSC can be explained because the angular sampling is very tight, i.e. 420 projections, so the two employed subtomograms in the FSC, each of 210 projections, were significantly undersampled compared to the number of voxels across the diameter of the sample. This means that the correlation between two such undersampled tomograms can give a low estimation of the spatial resolution. This feature is not observed for Syn-µCT and Lab-µCT as the total number of projections were 6000 and 1637, respectively. In other words, the subtomograms with half the number of projections were not undersampled for these two imaging modalities.
Etch-pit growth rate evaluation.
The estimation of the etch-pit growth rate was based on the analysis of 27 etch-pits from 5 different large alite grains. It is noted that the etch-pits have irregular 3D shapes and therefore, for its spatial dissolution rate estimation, some simplifications were undertaken. Moreover, the spatial resolution of this PXCT work, ∼250 nm, is limited for accurate analyses. Therefore, we consider this approach as an estimation. Firstly, etch-pits were visually selected from grains with sizes larger than 10 µm. Secondly, their overall shapes were compared in two hydrating steps. Then, two envelopes from pixels with at least 90% of the electron density of alite were developed. The estimated/calculated distance (in pixels) was computed between these edges for the deepest perpendicular length. These values were converted to dissolution rate by taking the ratio respect to the time between measurements. The result for the analysis between 19 and 47 h datasets gave 6.1 pixels of average distance which is equivalent to 41(29) nm/h. There was large variability in the rates, the fastest being 110 nm/h and the slowest being 10 nm/h. From this investigation, it is not possible to know if this large variability comes from the heterogeneity in the defects within these regions, or if other variables like the spatial resolution of this work and the local water-to-cement ratio variations are also playing important roles. More imaging studies are necessary to establish this. The very same 27 etch-pits were also analysed between 47 and 93 h datasets. In this case, the etch-pit growth rate was slower 7 nm/h, showing that the water diffusion is already limiting hydration at four days.

Water/cement ratio estimation of the scanned sample by PXCT
The w/c ratios of the scanned capillaries in a selected region can be calculated at the different ages according to the procedure previously reported 20 . The final β-mean values obtained by PXCT were used after converting to µ values, see Table S6. Then, using the mineralogical compositions of the anhydrous cement (given in the Supporting information, Table S2) the µ value is estimated, taking into account the µ value of free water, 22.2 cm -1 . For instance, for the 19 h sample, it can be estimated that the paste was composed of 69.9 wt% PC and 30.1 wt% water to account for the overall µ of the paste. This calculation yielded a w/c ratio of 0.39, see Table S6.

Chemical reactions
I. The chemical reactions used for the FW calculation, see Table S5, are: (1) the consumption of water by the hydration of C4AF, with C3S which is the source of silicates, to give amorphous iron siliceous hydrogarnet (Fe-Si-Hg) and crystalline portlandite; (2) the hydration of C3S to yield amorphous C-S-H gel and crystalline portlandite; (3) the hydration of C3A, consuming a calcium sulfate source, to yield ettringite if there are enough sulfates available (which is the case here); and (4) the possible carbonation of portlandite gives crystalline (and amorphous) calcium carbonate(s) and it releases free (capillary) water.
II. In the absence of belite hydration, the chemical reaction contributing to C-S-H gel formation, see Table  S5, is just (2). It is underlined that a small fraction of the consumed alite did not result in C-S-H gel but in the formation of iron siliceous hydrogarnet from the ferrite hydration (reaction 1).
It is noted here that for the calculations presented in Table S5, the amount of C3S which is needed for the silicate groups in iron-silicon-hydrogarnet, is calculated first from the degree of hydration of C4AF (applying reaction #1). Then, the portlandite and C-S-H gel contents are determined from the reaction of C3S after subtracting the number obtained in the process described just above.

Open access raw data availability and description
The following raw data has been openly deposited on Zenodo and can be acceded at: https://doi.org/10.5281/zenodo.7030107 1. Tomographic reconstructed raw data of all the X-ray imaging modalities (twelve tomograms) in 16 bit and .tif format. The size of the files is also given in the following

Particle size distribution (PSD)
"PSD" labelled folder contains two files in .mmes format.

Isothermal calorimetry
"Calorimetry" labelled folder contains six files in .xlsx excel format.

2.3) Laboratory X-ray powder diffraction (LXRPD)
"LXRPD" labelled folder contains five files in .ASC text format. Tables   Table S1. Chemical (elemental) analysis (by X-ray fluorescence) of the two employed Portland cements in this investigation. All data expressed in weight percentages of the corresponding oxides.   34 * This cement also has at t0: 1.4 wt% of gypsum, 1.4 wt% of bassanite and 0.6 wt% of quartz. & C-S-H, Fe-Si-Hg and FW (free water) contents calculated from the assumed chemical reactions as described in supplementary methods. # The calcite content increased from 2.0 wt% at t=0 to 3.6 wt% at 96 h, highlighting a significant carbonation of the paste within this large capillary, i.e. 1 mm of diameter. The thinner capillary used in the PXCT study, i.e. 0.2 mm of diameter, did not show a measurable conversion of CH to Cc, see below. Carbonation of a cement paste has been previously measured by PXCT, when its extension was significant. 22  Finally, β was calculated as = 4  Table S8. Component segmentation (vol%) and average electron densities obtained by PXCT at the different hydration ages; expected electron densities (from crystallographic data when it is possible) are also given for reference.  (4) -*Electron densities, from full volume, were obtained by segmentation excluding the external voxels to avoid partial volume effect & Electron densities, from particle picking, were obtained by the average of 10 cubes for the capillary; 5, 4, 5 and 6 grains for portlandite, calcium carbonate, alite and belite, respectively.            This series is intended to show the evolution of water porosity (dark-grey) towards air porosity (black) with time. Moreover, the enlarged views (right images) show the evolution of a small alite particle, initial size about 3 µm, which develops etch-pits of sizes of ∼700 nm, highlighted with red arrows.              (1) the hydration of a large alite particle with aluminoferrite, C4AF, intergrown, i.e. the whitest regions, see brown arrows. In addition to the etch-pit evolution, it can be seen that hydration stops at the regions where C4AF is exposed to the hydration medium; (2) the blue rectangles highlight the dissolution of C-S-H gel particles to give dry (air-filled) pores. Moreover, alite hydration also stops as soon as air porosity (pore drying) develops on the surfaces of the anhydrous grains, see red rectangles in the bottom panels. Figure S27. Selected PXCT vertical pictures with enlarged views (bottom) displaying the hydration pathway of a very fast dissolving particle, i.e. a 4 µm particle fully dissolved between 19 and 47 h. The electron density of this small volume, 0.91 e -Å -3 , is compatible with C3S or C3A. It already shows a gap at 19 h indicating a highly soluble component. At 47 h, two hydrate rods of diameter smaller than 1 µm, morphologically suggesting ettringite, grow in the pristine region which is filled with capillary water. At 93 h, the volume is fully occupied by hydrate(s). The dissolution rate between 19 and 43 h is faster than 75 nm/h suggesting C3A. However, the chemical nature of this tine particle could not be firmly established.
A summarized display of the cement paste hydration evolution as seen by this nanoimaging study. The progress of the different components is displayed after segmentation by Machine-Learning. Moreover, key changes like water porosity evolution or shrinkage development are highlighted on the video by embedded written text.
A video revealing the arrangement of the 3D segmented C-S-H shells through the 19 h nanoimaging dataset.
The size of each short video is standard 640×480 pixels in mp4 format as suggested by Nature journal. Therefore, users can download them quickly.

Article cover image:
Title: "X-ray nanoimaging of a hydrating cement paste at early ages" Description: The precipitating calcium silicate hydrate shells (blue) surround the dissolving alite particles (yellow) with regions of calcium aluminoferrite highlighted in orange. For better visualisation: only the C-S-H shells in the left part, the three components in the middle region, just the anhydrous cement particles in the right part. The gaps, approximately 500 nm, between the C-S-H shells and the dissolving alite particles are readily visible in the central part of the image.
The cover image is a high resolution 5000×4005 pixels size in .tif format.